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      Mathematical MethodsRemove Mathematical Methods →

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      • 2021
      • Working Paper

      How Much Should We Trust Staggered Difference-In-Differences Estimates?

      By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
      Difference-in-differences analysis with staggered treatment timing is frequently used to assess the impact of policy changes on corporate outcomes in academic research. However, recent advances in econometric theory show that such designs are likely to be biased in the... View Details
      Keywords: Difference In Differences; Staggered Difference-in-differences Designs; Generalized Difference-in-differences; Dynamic Treatment Effects; Mathematical Methods
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      Baker, Andrew C., David F. Larcker, and Charles C.Y. Wang. "How Much Should We Trust Staggered Difference-In-Differences Estimates?" European Corporate Governance Institute Finance Working Paper, No. 736/2021, February 2021. (Harvard Business School Working Paper, No. 21-112, April 2021.)
      • February 2021
      • Tutorial

      What is AI?

      By: Tsedal Neeley
      This video explores the elements that constitute artificial intelligence (AI). From its mathematical basis to current advances in AI, this video introduces students to data, tools, and statistical models that make a computer 'intelligent.' Through an explanation of... View Details
      Keywords: Artificial Intelligence; Digital; Technological Innovation; Leadership; AI and Machine Learning; Mathematical Methods
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      Neeley, Tsedal. What is AI? Harvard Business School Tutorial 421-713, February 2021. (https://hbsp.harvard.edu/product/421713-HTM-ENG?Ntt=tsedal%20neeley%20what%20is%20ai.)
      • February 2021
      • Article

      A Dynamic Theory of Multiple Borrowing

      By: Daniel Green and Ernest Liu
      Multiple borrowing—a borrower obtains overlapping loans from multiple lenders—is a common phenomenon in many credit markets. We build a highly tractable, dynamic model of multiple borrowing and show that, because overlapping creditors may impose default externalities... View Details
      Keywords: Commitment; Multiple Borrowing; Common Agency; Misallocation; Microfinance; Investment; Mathematical Methods
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      Green, Daniel, and Ernest Liu. "A Dynamic Theory of Multiple Borrowing." Journal of Financial Economics 139, no. 2 (February 2021): 389–404.
      • 2021
      • Article

      Prisoners, Rooms, and Lightswitches

      By: Daniel M. Kane and Scott Duke Kominers
      We examine a new variant of the classic prisoners and lightswitches puzzle: A warden leads his n prisoners in and out of r rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large number of times. The... View Details
      Keywords: Mathematical Methods
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      Kane, Daniel M., and Scott Duke Kominers. "Prisoners, Rooms, and Lightswitches." Electronic Journal of Combinatorics 28, no. 1 (2021).
      • 2021
      • Article

      Fair Algorithms for Infinite and Contextual Bandits

      By: Matthew Joseph, Michael J Kearns, Jamie Morgenstern, Seth Neel and Aaron Leon Roth
      We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. [2016], we carry out a more refined analysis of a more general problem, achieving better performance guarantees with fewer modelling assumptions... View Details
      Keywords: Algorithms; Bandit Problems; Fairness; Mathematical Methods
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      Joseph, Matthew, Michael J Kearns, Jamie Morgenstern, Seth Neel, and Aaron Leon Roth. "Fair Algorithms for Infinite and Contextual Bandits." Proceedings of the AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society 4th (2021).
      • January 2021
      • Article

      Using Models to Persuade

      By: Joshua Schwartzstein and Adi Sunderam
      We present a framework where "model persuaders" influence receivers’ beliefs by proposing models that organize past data to make predictions. Receivers are assumed to find models more compelling when they better explain the data, fixing receivers’ prior beliefs. Model... View Details
      Keywords: Model Persuasion; Analytics and Data Science; Forecasting and Prediction; Mathematical Methods; Framework
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      Schwartzstein, Joshua, and Adi Sunderam. "Using Models to Persuade." American Economic Review 111, no. 1 (January 2021): 276–323.
      • Article

      Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses

      By: Kaivalya Rawal and Himabindu Lakkaraju
      As predictive models are increasingly being deployed in high-stakes decision-making, there has been a lot of interest in developing algorithms which can provide recourses to affected individuals. While developing such tools is important, it is even more critical to... View Details
      Keywords: Predictive Models; Decision Making; Framework; Mathematical Methods
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      Rawal, Kaivalya, and Himabindu Lakkaraju. "Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses." Advances in Neural Information Processing Systems (NeurIPS) 33 (2020).
      • October 2020
      • Article

      Comparative Statics for Size-Dependent Discounts in Matching Markets

      By: David Delacretaz, Scott Duke Kominers and Alexandru Nichifor
      We prove a natural comparative static for many-to-many matching markets in which agents’ choice functions exhibit size-dependent discounts: reducing the extent to which some agent discounts additional partners leads to improved outcomes for the agents on the other side... View Details
      Keywords: Size-dependent Discounts; Path-independence; Respect For Improvements; Market Design; Mathematical Methods
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      Delacretaz, David, Scott Duke Kominers, and Alexandru Nichifor. "Comparative Statics for Size-Dependent Discounts in Matching Markets." Journal of Mathematical Economics 90 (October 2020): 127–131.
      • Oct 2020
      • Conference Presentation

      Optimal, Truthful, and Private Securities Lending

      By: Emily Diana, Michael J. Kearns, Seth Neel and Aaron Leon Roth
      We consider a fundamental dynamic allocation problem motivated by the problem of securities lending in financial markets, the mechanism underlying the short selling of stocks. A lender would like to distribute a finite number of identical copies of some scarce resource... View Details
      Keywords: Differential Privacy; Mechanism Design; Finance; Mathematical Methods
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      Diana, Emily, Michael J. Kearns, Seth Neel, and Aaron Leon Roth. "Optimal, Truthful, and Private Securities Lending." Paper presented at the 1st Association for Computing Machinery (ACM) International Conference on AI in Finance (ICAIF), October 2020.
      • 2020
      • Working Paper

      Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 6 The Value Structure of Technologies, Part 1: Mapping Functional Relationships

      By: Carliss Y. Baldwin
      Organizations are formed in a free economy because an individual or group perceives value in carrying out a technical recipe that is beyond the capacity of a single person. Technology specifies what must be done, what resources must be assembled, what actions taken in... View Details
      Keywords: Modularity; Information Technology; Organizations; Value Creation
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      Baldwin, Carliss Y. "Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 6 The Value Structure of Technologies, Part 1: Mapping Functional Relationships." Harvard Business School Working Paper, No. 21-039, September 2020.
      • September 2020 (Revised March 2022)
      • Case

      JOANN: Joannalytics Inventory Allocation Tool

      By: Kris Ferreira and Srikanth Jagabathula
      Michael Joyce, Vice President of Inventory Management at JOANN, championed an effort to develop and implement an inventory allocation analytics tool that used advanced analytics to predict in-season demand of seasonal items for each of JOANN’s nearly 900 stores and... View Details
      Keywords: Analytics; Machine Learning; Optimization; Inventory Management; Mathematical Methods; Decision Making; Operations; Supply Chain Management; Resource Allocation; Distribution; Technology Adoption; Applications and Software; Change Management; Fashion Industry; Consumer Products Industry; Retail Industry; United States; Ohio
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      Ferreira, Kris, and Srikanth Jagabathula. "JOANN: Joannalytics Inventory Allocation Tool." Harvard Business School Case 621-055, September 2020. (Revised March 2022.)
      • 2020
      • Working Paper

      Design and Analysis of Switchback Experiments

      By: Iavor I Bojinov, David Simchi-Levi and Jinglong Zhao
      In switchback experiments, a firm sequentially exposes an experimental unit to a random treatment, measures its response, and repeats the procedure for several periods to determine which treatment leads to the best outcome. Although practitioners have widely adopted... View Details
      Keywords: Switchback Experiments; Design; Analysis; Mathematical Methods
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      Bojinov, Iavor I., David Simchi-Levi, and Jinglong Zhao. "Design and Analysis of Switchback Experiments." Harvard Business School Working Paper, No. 21-034, September 2020.
      • 2020
      • Working Paper

      Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 5 Ecosystems and Complementarities

      By: Carliss Y. Baldwin
      The purpose of this chapter is to introduce two new building blocks to the theory of how technology shapes organizations. The first is a new layer of organization structure: a business “ecosystem.” The second is the economic concept of “complementarity.” Ecosystems are... View Details
      Keywords: Business Ecosystems; Complementarity; Modularity; Information Technology; Organizations
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      Baldwin, Carliss Y. "Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 5 Ecosystems and Complementarities." Harvard Business School Working Paper, No. 21-033, August 2020.
      • August 2020 (Revised September 2020)
      • Technical Note

      Assessing Prediction Accuracy of Machine Learning Models

      By: Michael W. Toffel, Natalie Epstein, Kris Ferreira and Yael Grushka-Cockayne
      The note introduces a variety of methods to assess the accuracy of machine learning prediction models. The note begins by briefly introducing machine learning, overfitting, training versus test datasets, and cross validation. The following accuracy metrics and tools... View Details
      Keywords: Machine Learning; Statistics; Econometric Analyses; Experimental Methods; Data Analysis; Data Analytics; Forecasting and Prediction; Analytics and Data Science; Analysis; Mathematical Methods
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      Toffel, Michael W., Natalie Epstein, Kris Ferreira, and Yael Grushka-Cockayne. "Assessing Prediction Accuracy of Machine Learning Models." Harvard Business School Technical Note 621-045, August 2020. (Revised September 2020.)
      • August 2020
      • Technical Note

      Comparing Two Groups: Sampling and t-Testing

      By: Iavor I Bojinov, Chiara Farronato, Yael Grushka-Cockayne, Willy C. Shih and Michael W. Toffel
      This note describes sampling and t-tests, two fundamental statistical concepts. View Details
      Keywords: Statistics; Econometric Analyses; Experimental Methods; Data Analysis; Data Analytics; Analytics and Data Science; Analysis; Surveys; Mathematical Methods
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      Bojinov, Iavor I., Chiara Farronato, Yael Grushka-Cockayne, Willy C. Shih, and Michael W. Toffel. "Comparing Two Groups: Sampling and t-Testing." Harvard Business School Technical Note 621-044, August 2020.
      • Article

      Matching in Networks with Bilateral Contracts: Corrigendum

      By: John William Hatfield, Ravi Jagadeesan and Scott Duke Kominers
      Hatfield and Kominers (2012) introduced a model of matching in networks with bilateral contracts and showed that stable outcomes exist in supply chains when firms' preferences over contracts are fully substitutable. Hatfield and Kominers (2012) also asserted that in... View Details
      Keywords: Matching With Contracts; Substitutability; Mathematical Methods
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      Hatfield, John William, Ravi Jagadeesan, and Scott Duke Kominers. "Matching in Networks with Bilateral Contracts: Corrigendum." American Economic Journal: Microeconomics 12, no. 3 (August 2020): 277–285.
      • Article

      Oracle Efficient Private Non-Convex Optimization

      By: Seth Neel, Aaron Leon Roth, Giuseppe Vietri and Zhiwei Steven Wu
      One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it.... View Details
      Keywords: Machine Learning; Algorithms; Objective Perturbation; Mathematical Methods
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      Neel, Seth, Aaron Leon Roth, Giuseppe Vietri, and Zhiwei Steven Wu. "Oracle Efficient Private Non-Convex Optimization." Proceedings of the International Conference on Machine Learning (ICML) 37th (2020).
      • Article

      Active World Model Learning with Progress Curiosity

      By: Kuno Kim, Megumi Sano, Julian De Freitas, Nick Haber and Daniel Yamins
      World models are self-supervised predictive models of how the world evolves. Humans learn world models by curiously exploring their environment, in the process acquiring compact abstractions of high bandwidth sensory inputs, the ability to plan across long temporal... View Details
      Keywords: World Models; Mathematical Methods
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      Kim, Kuno, Megumi Sano, Julian De Freitas, Nick Haber, and Daniel Yamins. "Active World Model Learning with Progress Curiosity." Proceedings of the International Conference on Machine Learning (ICML) 37th (2020).
      • 2021
      • Conference Presentation

      An Algorithmic Framework for Fairness Elicitation

      By: Christopher Jung, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton and Zhiwei Steven Wu
      We consider settings in which the right notion of fairness is not captured by simple mathematical definitions (such as equality of error rates across groups), but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders.... View Details
      Keywords: Algorithmic Fairness; Machine Learning; Fairness; Framework; Mathematical Methods
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      Jung, Christopher, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton, and Zhiwei Steven Wu. "An Algorithmic Framework for Fairness Elicitation." Paper presented at the 2nd Symposium on Foundations of Responsible Computing (FORC), 2021.
      • May 2020
      • Article

      Identifying Sources of Inefficiency in Health Care

      By: Amitabh Chandra and Douglas O. Staiger
      In medicine, the reasons for variation in treatment rates across hospitals serving similar patients are not well understood. Some interpret this variation as unwarranted and push standardization of care as a way of reducing allocative inefficiency. However, an... View Details
      Keywords: Health Care and Treatment; Performance Efficiency; Performance Productivity; Mathematical Methods
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      Chandra, Amitabh, and Douglas O. Staiger. "Identifying Sources of Inefficiency in Health Care." Quarterly Journal of Economics 135, no. 2 (May 2020): 785–843.
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